Distributions are considered any population that has a scattering of data. It’s important to determine the kind of distribution that population has so we can apply the correct statistical methods when analyzing it.

Types of Data in a Distribution

Typically discreet or continuous

Discrete Distributions

Discrete= counted

Continuous Distributions

Continuous = can take many different values

Non-normal distributions

Also see Non-normal distributions

 Evaluating a Distribution

  • Look for hard stops
  • # of values
  • Evaluate the shape
    • Exponential – hockey stick
      • Has a constant failure rate as it will always have the same shape parameters.
    • Gamma
      • Contains variable shape and scale parameters.
    • Uniform – Flat bar, constant: used to test random # generators- everything has the same probability.
    • Log-normal (lognormal)– Used in maintainability analysis – bringing broken tools back on line tends to follow lognormal.
      • takes on different shapes depending on the mean and standard deviation.
      • http://www.free-six-sigma.com/lognormal-distribution.html (Lognormal distribution)
    • Bi-modal – 2 sources of data coming into a single process screen.
    • Weibull
      • Assumes many shapes depending upon the shape, scale, and location parameters.Effect of Shape parameter B on Weibull distribution:

Symmetric Distribution

Both sides of the mean match & mirror each other.

Asymmetric Distribution

Both sides of the mean do NOT match.

Skewed Distribution

The data set has outliers. Skewness is a measure of the lack of symmetry.

When the outliers are high on one side, the mean will be > Median

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